1. Field of the Invention
The present invention relates to signal processing, and, in particular, to the processing of noisy received signals, such as high-speed optical signals distorted by linear and non-linear polarization mode dispersion (PMD) effects during transmission through an optical transmission path and resulting in data pulse broadening and inter-symbol interference (ISI).
2. Description of the Related Art
As transmission speed increases in optical fiber communications, polarization mode dispersion (PMD) becomes a significant factor limiting system performance, especially for transmission speeds of 10 Gb/s or higher. PMD causes data pulse broadening and creates inter-symbol interference (ISI). Unlike chromatic dispersion which can usually be countered by using a short dispersion-compensated fiber, PMD is time varying. While optical solutions have been proposed to counter PMD, they are usually very expensive and require a feedback path from the receiver back to the transmitter.
Traditionally, electronic adaptive equalizers have been used to mitigate received signal distortion resulting in ISI. Well-known techniques for channels having linear distortion include linear feedforward equalization and linear decision feedback equalization (DFE).
FIG. 1 shows a conventional equalizer 100 used to correct linear signal distortion. Equalizer 100 has two adaptive equalizers: adaptive equalizer 102 configured to provide feedforward equalization and adaptive equalizer 104 configured to provide decision feedback equalization. In particular, adaptive equalizer 102 receives the current received signal νin and generates a linearly equalized signal νin′. This equalized signal νin′ is presented to subtraction node 106, which subtracts the feedback signal generated by adaptive equalizer 104. The resulting difference signal is presented to slicer 108, which decides whether the current received signal νin corresponds to a “1” or a “0” by comparing the difference signal to a fixed threshold between 0 and 1 (e.g., half way between the reference voltages for logic “1” and logic “0” inside the slicer). The selected output data level is fed back to adaptive equalizer 104. In addition, the error signal (i.e., the difference between the difference signal generated at subtraction node 106 and the sliced signal level generated by slicer 108) is fed back to both adaptive equalizers 102 and 104 and used to dynamically control the coefficients within those equalizers using some conventional technique such as a least mean square (LMS) algorithm. Further information about typical implementations of adaptive equalizers 102 and 104 can be found in E. A. Lee and D. G. Messerschmitt, Digital Communication, Kluwer Academic Publisher, 1988, and S. U. H. Qureshi, “Adaptive Equalization,” Proceedings of the IEEE, Vol. 73, No. 9, September 1985, the teachings of both of which are incorporated herein by reference.
When the channel is non-linear, such as an optical fiber channel dominated by PMD effects, non-linear equalization is used, since the effectiveness of equalizers, such as that shown in FIG. 1, is limited in those cases. Non-linear equalization techniques range from extremely complex solutions, such as those described in U.S. Pat. No. 4,213,095, to simple single-tap non-linear DFE modules, such as those described in U.S. Pat. No. 5,191,462.
In general, effective non-linear equalization is a very complex and difficult process, involving the inversion of the non-linear channel response such that the combined channel and non-linear equalizer frequency response is flat. The optimization cost functions are often not smooth convex functions and, as a result, considerable adaptation convergence difficulties exist. These difficulties are manifested by the complexity of the techniques described in U.S. Pat. No. 4,213,095.